Mitigation of Classes of Attacks using a Probabilistic Discrete Event System Framework

Cyber-attack models and their respective mitigation strategies have been recently studied in the discrete event systems setting. Previous work focuses on whether unsafe behaviour can be prevented using supervisory control theory. When unsafe behaviour cannot be prevented with certainty, mitigation strategies are limited. This paper proposes the use of a probabilistic discrete event system (PDES) framework to incorporate a likelihood measure for unsafe behaviour in the attack models presented in Carvalho et al. (2018). The least-unsafe (LU) supervisor problem is introduced to minimize this unsafe likelihood measure and improve existing attack mitigation techniques. The LU supervisor problem under full observability is solved by reformulating it into an MDP problem, and a computable algorithm is developed. Lastly, the implementation of LU supervisors is discussed and illustrated with an example.